Method and apparatus for channel estimation of transmission channels with memory in digital telecommunications systems, and corresponding computer-program product

ABSTRACT

In order to execute, as a function of a received signal (r), a procedure of channel estimation in a transmission channel with memory in a telecommunications system, there is envisaged an operation of estimation of a delay spread associated to said channel, said operation of estimation comprising calculation of a root mean square value (τ rms ) of delay spread by means of a step of evaluation of crossings with a threshold level of a quantity associated to a transfer function of said channel. Said step of evaluation of crossings comprises evaluating a mean number of crossings (λ 0 ) of the real and imaginary parts of said channel transfer function with a threshold level corresponding to the zero level. Example application is to OFDM telecommunications systems and in particular wireless systems according to the IEEE 802.11a WLAN standard or the Hyperlanll WLAN standard.

TECHNICAL FIELD

The present disclosure generally relates to telecommunicationstechniques and has been developed with particular but not exclusiveattention paid to its possible application to digital telecommunicationssystems based upon a modulation of an orthogonal frequency-divisionmultiplexing (OFDM) type.

Although in what follows, for reasons of clarity and simplicity ofexposition, almost exclusive reference will be made to this application,it is in any case to be borne in mind that the scope of this disclosureis more general. The disclosure is in fact applicable to alltelecommunications systems in which there occur conditions of operationof the same type as the ones described in what follows.

BACKGROUND INFORMATION

In digital telecommunications systems and in particular intelecommunications systems of a wireless type, there are oftenencountered transmission channels with memory. Said transmissionchannels with memory bring about a spread in time of the transmittedsignal. In the frequency domain, said phenomenon produces the so-calledfrequency selectivity. It is crucial in these cases to know the amountof said spread, which is often characterized by a so-called delay-spreadtime. The knowledge of the delay spread enables among other thingsadaptive calibration of the channel-estimation algorithms. Saidalgorithms must estimate a number of parameters proportional to thedelay spread. In the case where this is unknown, the channel estimatorsmust be parameterized in a conservative way, e.g., presupposing alwayshaving the maximum delay spread that can be supported by the system.Said assumption has as an effect a reduction in the overall performanceof the system.

In greater detail, a transmission channel with memory is characterizedby an impulse response h(τ) of the type: $\begin{matrix}{{h(\tau)} = {\sum\limits_{i = 0}^{L - 1}{h_{i} \cdot {\delta\left( {\tau - \tau_{i}} \right)}}}} & (1)\end{matrix}$where h_(i) indicates a complex number (which is possibly time variant)that represents a gain applied to the replica of the received signalwith a delay t_(i), and L represents the number of distinguishablereplicas. The gains h_(i) are complex Gaussian random variables withzero mean. In some cases the gain h₀ can have a mean other than zero.Said channels are referred to as Rice channels.

A corresponding transfer function H(ƒ) of the impulse response h(τ) ofthe transmission channel with memory is obtained by applying the Fouriertransform: $\begin{matrix}{{H(f)} = {{\int_{- \infty}^{+ \infty}{{{h(\tau)} \cdot {\mathbb{e}}^{{- {j2}}\quad{\pi f}\quad\tau}}\quad{\mathbb{d}\tau}}} = {\sum\limits_{i = 0}^{L - 1}{{h_{i} \cdot {\mathbb{e}}^{{- {j2}}\quad\pi\quad f\quad\tau_{i}}}{\mathbb{d}\tau}}}}} & (2)\end{matrix}$A power delay profile (PDP), P(τ), is defined as: $\begin{matrix}{{P(\tau)} = {\sum\limits_{i = 0}^{L - 1}{{E\left\lbrack {h_{i}^{2}} \right\rbrack} \cdot {\delta\left( {\tau - \tau_{i}} \right)}}}} & (3)\end{matrix}$where for reasons of simplicity${\sum\limits_{i = 0}^{L - 1}{E\left\lbrack {h_{i}^{2}} \right\rbrack}} = 1.$

Defined as mean square deviation of the delay spread, or root meansquare delay spread (RMS-DS) and designated by τ_(rms) is the followingquantity: $\begin{matrix}{\tau_{rms} = \sqrt{{\sum\limits_{i}{{h_{i}}^{2}\tau_{i}^{2}}} - \left( {\sum\limits_{i}\left( {{h_{i}}^{2} \cdot \tau_{i}} \right)} \right)^{2}}} & (4)\end{matrix}$

The RMS-DS τ_(rms) provides a quantitative measurement of the degree ofdelay spread produced by the channel. Its inverse provides, instead, ameasurement of the coherence band of the channel itself. This representsthe bandwidth that incurs the same type of distortion by the channel. Itis evident that the greater the dispersion of the channel the smallerwill be the coherence band and consequently the more the channel will beselective in frequency.

The knowledge of the RMS-DS τ_(rms) hence indirectly provides a tool forselecting the unknown parameters of the impulse response h(τ) or of itstransform H(ƒ); for example, assuming a delay profile P(τ) of anexponential type it is possible to obtain an estimation of the maximumsignificant delay t_(L−1).

Among the solutions known in the state of the art, the most commonmethod for parameter estimation in OFDM systems is the one proposed inthe publication O. Edfors, M. Sandell, J. van de Beek, S. K. Wilson, P.Berjesson, “OFDM Channel Estimation by singular value decomposition”,IEEE Transactions on Communications, vol. 46, No. 7 July 1998, where inparticular singular-value decomposition of the correlation matrix of thechannel frequency response is used. In this case, the computational costis significant. Likewise, in O. Simeone, Y. Bar-Ness, U. Spagnolini,“Subspace-tracking methods for channel estimation in OFDM systems”, IEEETransactions on Wireless Communications, vol. 3, no. 1, January, 2004,estimation of the rank of the correlation matrix of the channel transferfunction is exploited. Also in this case, the computational costs areother than negligible.

Another technique regarding estimation of the RMS-DS τ_(rms) is proposedin the publication Wu S., Bar-Ness Y., “OFDM Channel Estimation in thepresence of frequency offset and phase noise”, IEEE InternationalConference on Communications, ICC '03, Volume 5, May 11-15, 2003, andenvisages using an iterative technique for the search for the optimallength of the channel delay profile. The technique comprises seeking thesupport of the channel delay profile (which is proportional to the delayspread) increasingly from 1 to the length of the cyclic prefix of theOFDM symbol. At each iteration, two conditions are verified, whichcompare the improvement obtained in the estimation of the delay profilewith respect to the previous iteration. The length of the support isdetermined from the outcome of the two comparisons. The latency andcomputational costs of this approach are evident.

A method for estimating the delay-spread value is known from thepublications: K. Witrisal, Y. Kim, R. Prasad, “A new method to measureparameters of frequency-selective radio channels using powermeasurements”, IEEE Transactions on Communications, vol. 49, No. 10,October 2001; and K. Witrisal, “On estimating the RMS Delay Spread fromthe frequency domain level crossing rate”, 2001, IEEE Comm. Letters,Vol. 5, No. 7, pp. 3366-3370. Said method is based upon theproportionality between the density of crossings of the envelope of thechannel transfer function with a pre-selected level and the RMS-DSτ_(rms) itself. The method described in the above documents has beendeveloped in a context of statistical characterization of radio channelsin order to provide designers of wireless telecommunications systemswith realistic channel models. Said method, however, involvespre-selecting an adequate level and is sensitive to noise.

BRIEF SUMMARY OF THE INVENTION

One embodiment of the present invention provides a solution capable ofperforming the functions described previously in a simpler manner, withlow computational cost and with low sensitivity to noise.

According to an embodiment of the present invention, the above purposeis achieved by a method having the characteristics described herein.Embodiments of the invention also relate to the corresponding apparatus,as well as to a computer-program product directly loadable into thememory of a computer and comprises software code portions for performingthe method when the product is run on a computer.

A solution according to one embodiment of the invention envisagesestimating the delay spread of a channel with memory, starting from themean number of zero crossings of the real part and of the imaginary partof the channel transfer function itself.

As compared to the known solutions, the solution proposed herein has theadvantage of being extremely simple and particularly effective whenassociated with systems with modulation of an OFDM type, where apreliminary estimate of the channel transfer function is usuallyavailable. From this, it is possible to determine the delay spread andsubsequently proceed to a more reliable channel estimation thanks to thereduction in the number of unknown parameters.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

Embodiments of the invention will now be described, purely by way of oneor more non-limiting examples, with reference to the annexed drawings,in which:

FIG. 1 shows an OFDM transmitter designed to implement one embodiment ofthe method according to the invention;

FIG. 2 shows an OFDM receiver designed to implement the procedure ofchannel estimation according to an embodiment of the invention;

FIG. 3 represents an embodiment of the receiver of FIG. 2; and

FIG. 4 represents a detail of the embodiment of FIG. 3.

DETAILED DESCRIPTION

In the following description, certain specific details are set forth inorder to provide a thorough understanding of various disclosedembodiments. However, one skilled in the relevant art will recognizethat embodiments may be practiced without one or more of these specificdetails, or with other methods, components, materials, etc. In otherinstances, well-known structures have not been shown or described indetail to avoid unnecessarily obscuring descriptions of the embodiments.

Unless the context requires otherwise, throughout the specification andclaims which follow, the word “comprise” and variations thereof, suchas, “comprises” and “comprising” are to be construed in an open,inclusive sense, that is, as “including, but not limited to.”

Reference throughout this specification to “one embodiment” or “anembodiment” means that a particular feature, structure or characteristicdescribed in connection with the embodiment is included in at least oneembodiment. Thus, the appearances of the phrases “in one embodiment” or“in an embodiment” in various places throughout this specification arenot necessarily all referring to the same embodiment. Further more, theparticular features, structures, or characteristics may be combined inany suitable manner in one or more embodiments.

The embodiment(s) of the method proposed envisages estimating the delayspread of a channel with memory on the basis of the mean number of zerocrossings of the real part and imaginary part of the transfer functionof said channel.

Described in what follows is the construction of the estimator used inthe method, in the condition of absence of noise.

As demonstrated in Papoulis A., “Probability, Random Variables andStochastic Processes”, McGraw-Hill, Third Edition, the square of adensity of crossings A of a random Gaussian process with zero mean witha level a, if said level a corresponds to zero, is equal to:$\begin{matrix}{\lambda_{0}^{2} = {\frac{- {R^{''}(0)}}{\pi^{2}{R(0)}} = \frac{\int_{- \infty}^{+ \infty}{\omega^{2}{S_{x}(\omega)}{\delta\omega}}}{\pi^{2}{\int_{- \infty}^{+ \infty}{{S_{x}(\omega)}{\delta\omega}}}}}} & (5)\end{matrix}$

Designated in what follows by λ₀ will hence be a density of zerocrossings.

The development of an estimator for the RMS-DS τhd rms is based uponEquation (5). The process whereof the density of zero crossings can becalculated is the channel frequency response H(ƒ). It can be shown thatthe power spectral density S_(H)(ω) of the process having a frequencyresponse H(ƒ) is: $\begin{matrix}{{S_{H}(\omega)} = {\sum\limits_{i = 0}^{L - 1}{{E\left\lbrack {h_{i}}^{2} \right\rbrack}{\delta\left( {\tau_{i} + \omega} \right)}}}} & (6)\end{matrix}$namely, said spectral density S_(H) (ω) is represented by the delayprofile with the axis of the delays r reversed, as can be readily notedfrom a comparison between Equation (6) and Equation (3).

Typically a delay profile has a decreasing exponential behavior, asshown by the following expression: $\begin{matrix}{{{h(\tau)}}^{2} = {\frac{1}{\tau_{rms}}{\mathbb{e}}^{- \frac{\tau}{\tau_{rms}}}}} & (7)\end{matrix}$

As demonstrated by Equation (6), the delay profile coincides with thepower spectral density expressed in the frequency domain.

There can now be applied to this case Equation (5), to obtain for thesquare λ₀ ² of a density of crossings λ with the zero level:$\begin{matrix}{\lambda_{0}^{2} = {\frac{\int_{0}^{\infty}{{\omega^{2} \cdot \frac{1}{\tau_{rms}} \cdot {\mathbb{e}}^{- \frac{w}{2{\pi\tau}_{rms}}}}\quad{\mathbb{d}\omega}}}{\pi^{2}{\int_{0}^{\infty}{{\frac{1}{\tau_{rms}} \cdot {\mathbb{e}}^{- \frac{w}{2{\pi\tau}_{rms}}}}\quad{\mathbb{d}\omega}}}} = {8\tau_{tms}^{2}}}} & (8)\end{matrix}$

By inverting Equation (8) the following expression for the RMS-DSτ_(rms) can be obtained: $\begin{matrix}{\tau_{rms} = {\frac{1}{\sqrt{8}}\lambda_{0}}} & (9)\end{matrix}$

It may be noted that the process H(ƒ) is, in general, complex;consequently, two independent measurements of density of zero crossingsλ₀ can be obtained considering separately the real part and theimaginary part of said process H(ƒ).

Designated by λ_(0re) is hence the density of zero crossingscorresponding to the real part of the process H(ƒ), whilst designated byλ_(0im) is the density of zero crossings for the imaginary part of theprocess H(ƒ).

The final estimation of the RMS-DS τ_(rms) is obtained by taking themean of said two densities of zero crossings: $\begin{matrix}{\tau_{rms} = {\frac{1}{\sqrt{8}}\left( \frac{\lambda_{0{re}} + \lambda_{0{im}}}{2} \right)}} & (10)\end{matrix}$

Described hereinafter is the construction of the estimator used in themethod, considering, however, the effect of the noise present on thefrequency response H(ƒ).

The density of zero crossings λ₀ measured is in fact greater on accountof the presence of the noise. Consequently, the estimator obtainedpreviously according to Equation (10) would yield an overestimate of thevalue of RMS-DS τ_(rms).

If the noise is not correlated to the signal, its power spectral densityS_(N) (ω) is added to the one already calculated in Equation (6), toobtain a power spectral density S(ω):S(ω)=S _(H)(ω)+S _(N)(ω)   (11)

Assuming a white Gaussian noise with variance η_(N) ² the power spectraldensity of the noise S_(N) (ω) is constant.

It is assumed moreover that both the delay profile and the noise arelow-pass filtered in the domain r to eliminate a part of noise via afilter H_(filter) (τ) with constant response up to τ=τ_(MAX), which isthe maximum allowable length of the delay profile.

With these assumptions, it is possible to recalculate the density ofzero crossings: $\begin{matrix}{{\lambda_{0}^{2} = {\frac{\int_{- \infty}^{+ \infty}{\omega^{2}{S(\omega)}\quad{\mathbb{d}\omega}}}{\pi^{2}{\int_{- \infty}^{+ \infty}{{S(\omega)}\quad{\mathbb{d}\omega}}}} = {\frac{\int_{- \infty}^{+ \infty}{{\omega^{2}\left( {{S_{H}(\omega)} + {S_{N}(\omega)}} \right)}\quad{\mathbb{d}\omega}}}{\pi^{2}{\int_{- \infty}^{+ \infty}{\left( {{S_{H}(\omega)} + {S_{N}(\omega)}} \right)\quad{\mathbb{d}\omega}}}} = \frac{{2 \cdot {SNR} \cdot I_{H}^{(2)}} + I_{N}^{(2)}}{\pi^{2}\left( {{2 \cdot {SNR} \cdot I_{H}^{(0)}} + I_{N}^{(0)}} \right)}}}}{{where}:}} & (12) \\{{SNR} = \frac{\sigma_{H}^{2}}{\sigma_{N}^{2}}} & (13) \\{I_{H}^{(n)} = {\int_{- \infty}^{+ \infty}{\omega^{n}{S_{H}(\omega)}{{H_{filter}(\omega)}}^{2}\quad{\mathbb{d}\omega}}}} & (14) \\{I_{N}^{(n)} = {\int_{- \infty}^{+ \infty}{\omega^{n}{{H_{filter}(\omega)}}^{2}\quad{\mathbb{d}\omega}}}} & (15)\end{matrix}$

On account of how the filter H_(filter) (τ) is constructed, it may beassumed that I_(H) ⁽⁰⁾=1.

By inverting Equation (12) and assuming available a measurement of thedensity of zero crossings A ₀ calculated as in Equation (10), thefollowing relation for estimation of the RMS-DS τ_(rms) is obtained:$\begin{matrix}{{\hat{I}}_{H}^{(2)} = {{{\hat{\lambda}}_{0}^{2} \cdot \pi^{2}} - \frac{I_{N}^{(2)} - {{\hat{\lambda}}_{0}^{2} \cdot \pi^{2} \cdot I_{N}^{(0)}}}{2 \cdot {SNR}}}} & (16)\end{matrix}$

The second term of Equation (16) represents a corrective factor thattakes into account the contribution of noise on the calculation of zerocrossings. The term is proportional to the inverse of thesignal-to-noise ratio SNR.

It is now possible to calculate the RMS-DS τ_(rms) as $\begin{matrix}{\tau_{rms} = {\frac{1}{\pi} \cdot \sqrt{\frac{{\hat{I}}_{H}^{(2)}}{8}}}} & (17)\end{matrix}$

It is clear that the extension of the proposed method just described todelay profiles of other forms is to be considered as readily deduciblefrom the one just described.

It may be noted that, in general, the exact shape of the delay profileis not known. It is, however, reasonable to assume in the case ofchannels with memory of a wireless type a distribution of an exponentialtype. Each time, according to the information a priori on the channel,it will be useful to assume the most appropriate form of the PDP. Itshould be noted that for the cases of interest, a direct proportionalitybetween the RMS-DS τ_(rms) and the density of zero crossings is alwaysfound.

The embodiment(s) of the method described above has a practicallynegligible complexity and can hence be exploited in particular intelecommunications systems with a modulation of an OFDM type, such asfor example the U.S. WLAN standard IEEE 802.11a and the European WLANstandard Hyperlanll.

Briefly described hereinafter is an example structure of an OFDMtelecommunications system in order to clarify to which part of thesystem the method and apparatus according to embodiments of theinvention are applied and how they achieve their technical effect.

In OFDM modulation a high-bitrate data flow is split into a number oflower-bitrate flows, which are transmitted in parallel on a number ofsubcarriers that are orthogonal to one another. An available band B isthus split into an integer number N of equispaced subcarriers that areorthogonal to one another as long as the following condition isrespected as regards their spacing in frequency Δƒ: $\begin{matrix}{{\Delta\quad f} = {\frac{B}{N} = \frac{1}{T_{s}}}} & (18)\end{matrix}$where T_(S) indicates the duration of the OFDM symbol.

Said condition can be readily obtained via an inverse discrete Fouriertransform. The number N of subcarriers is chosen normally as a power oftwo, so as to enable use of efficient implementations of the directFourier transform (Fast Fourier Transform—FFT) and of said inverseFourier transform (Inverse Fast Fourier Transform—IFFT). Theintroduction of a cyclic prefix “periodicizes” the signal transmitted,rendering the system robust in regard to the delay spread introduced bythe radio channel.

The data flow that it is to be transmitted is modulated through theclassical modulations (PSK, QPSK or QAM) to obtain a sequence of complexnumbers d_(k). Via an inverse transform of an IFFT type, a signal in thetime domain x[n] is obtained: $\begin{matrix}{{{x\lbrack n\rbrack} = {{\frac{1}{N}{\sum\limits_{k = 0}^{N - 1}{d_{k}{\mathbb{e}}^{j\frac{2\pi\quad k\quad n}{N}}\quad n}}} = 0}},1,\ldots\quad,{N - 1}} & (19)\end{matrix}$

Before performing transmission, there is set in front of each symbol thelast part of the symbol itself (cyclic prefix) so as to preventintroduction of intersymbol interference and guarantee orthogonalitybetween the subcarriers. Reference in this regard may be made to FIG. 1,which shows an OFDM transmitter, designated as a whole by the referencenumber 100, which comprises a serial-to-parallel converter 105, whichreceives at input the sequence of complex numbers d_(k) and supplies itin parallel to a block 110, which symbolically represents an IFFToperation, designed to generate at output in parallel the N symbols ofthe signal in the time domain x[n], added to which, in a block foraddition of the cyclic prefix 115, is the last part of the symbolitself. At output from the block for addition of the cyclic prefix 115there is then set a parallel-to-serial converter 120 for serializing thesequence to be transmitted g.

The receiver for an OFDM system, after determining the synchronizationpoint, eliminates the cyclic prefix and executes the discrete Fouriertransform on the N remaining samples y[n] to obtain a received signal:$\begin{matrix}{{{Y\lbrack k\rbrack} = {{\sum\limits_{n = 0}^{N - 1}{{y\lbrack n\rbrack}{\mathbb{e}}^{{- j}\frac{2\pi\quad{kn}}{N}}}} = {{{{H(k)} \cdot d_{k}} + {{n(k)}\quad k}} = 0}}},1,{{\ldots\quad N} - 1}} & (20)\end{matrix}$

Accordingly, FIG. 2 shows an OFDM receiver, designated as a whole by thereference number 200, which converts a demodulated received sequence rfrom serial into parallel in a corresponding serial-to-parallelconverter 205 and eliminates the cyclic prefix thereof from the symbolsin a module for elimination of the cyclic prefix 210, so producing the Nsamples y[0] . . . y[N−1] of the received sequence, which aretransformed, in a block 215 which carries out the FFT, into thecoefficients Y[0] . . . Y[N−1] of the received signal Y[k]. Then, aparallel-to-serial converter 220 produces the received signal Y[k]. Saidreceived signal Y[k], but for the noise, is equal to the desired signalmultiplied by the frequency response of the channel. The distortingeffect of the radio channel can be conveniently removed in the frequencydomain provided that a reliable channel estimate is available.

One example embodiment of the method proposed in OFDM telecommunicationssystems hence finds application mainly in the context of channelestimation.

There will now be described an embodiment of an estimator according tothe method proposed in WLAN systems operating according to the standardIEEE 802.11a and with OFDM modulation. Said systems envisage packettransmission. The data part is preceded by a preamble known to thereceiver, said preamble being useful for estimating some parameters ofthe channel, among which the frequency response.

A simplified scheme of a digital section, designated by the referencenumber 400, of an IEEE 802.11a WLAN receiver is represented in FIG. 3,where the reference number 405 designates a module for compensation ofRF defects, said module receiving digital data r_(d) from ananalog-to-digital converter (not shown in the figure) and supplies itsoutput to a module for compensation of the carrier-frequency offset(CFO) 410. In this way, the signal is cleaned from the distortions dueto the RF stages. Set downstream of said module 410 is a module 415 forperforming an FFT operation, which is followed by a module 420 for CFOcompensation in the frequency domain, and by an equalizer 425, whichsupplies an equalized signal. The equalized signal is demodulated, andthe likelihoods of the individual bits are extracted in a slicing anddemapping block 430 and finally is a Viterbi decoder 440.

At the same time, preambles p taken from the digital data r_(d) by theanalog-to-digital converter are moreover sent in parallel to the inputof a module 445 for synchronization, CFO estimation, and estimation ofthe signal-to-noise ratio (SNR). The CFO estimate is supplied to themodule for CFO compensation 410, whilst the SNR estimate is supplied toa channel-estimator block 450 together with the preambles p. Saidchannel-estimator block 450 supplies at output an estimate of thechannel Ĥ(ƒ), which is sent to the equalizer 425 and to a module forfine estimation of the CFO 455. Said module for fine estimation of theCFO 455 provides information on a residual carrier-frequency offset(RCFO) to the module 420 for its compensation in the frequency domain.The equalizer 425 compensates the distortions due to the transmissionchannel thanks to the estimation of the channel transfer functionproduced by the channel-estimator block 450. From the signals equalizedthe likelihoods of the transmitted bits are extracted by block 430.These are sent to the Viterbi decoder 440, which supplies thetransmitted data.

The channel-estimator block 450 is represented in greater detail in FIG.4 and comprises a first block 451, which executes a first roughestimation Ĥ′(ƒ) of the channel frequency response by demodulating thesignal received at the preamble (maximum-likelihood or ML estimation).If there is available a first rough estimate Ĥ′(ƒ) of the channelfrequency response, it is possible to evaluate, in a block forestimation of the RMS-DS 452, the estimate of the RMS-DS τ_(rms), asdescribed previously with reference to Equation (17). Once the estimateof the RMS-DS τ_(rms) has been obtained, in an fine-channel-estimationblock 453 further processing can be performed on the estimate Ĥ′(ƒ) toobtain a more reliable estimate Ĥ(ƒ).

The solution just described enables considerable advantages to beachieved with respect to known solutions.

The embodiment(s) of the method proposed advantageously envisagesestimating the delay spread of a channel with memory, starting from themean number of zero crossings of the real part and imaginary part of thetransfer function of said channel. Said solution presents the advantageof being extremely simple if compared with the solutions that use thedensity of crossings, with a pre-selected level, of a characteristiccurve of the channel transfer function, said characteristic curve beingrepresented by the envelope of the transfer function itself instead ofby its real and imaginary parts, as in the method proposed. In fact, theembodiment(s) of the proposed method in this way advantageously does notinvolve having, in the first place, to pre-select a threshold level withrespect to which the crossings are to be calculated, and in the secondplace it is advantageously able to eliminate any possible biasing of themeasurement due to the presence of noise. The separate analyses of thereal and imaginary parts enable two observations of the same physicalquantity, which inevitably leads to an improvement of the measurementvia a simple averaging operation.

The embodiment(s) of the method proposed is moreover particularlyadvantageous when implemented in a channel estimator in the framework ofan OFDM system.

It may moreover be noted that in OFDM systems, the most widespreadmethod of estimation of the delay spread requires singular-valuedecomposition of the matrix or at least an estimation of the rank of theautocorrelation matrix of the channel transfer function. Both of theoptions are considerably more complex than one embodiment of the methodand apparatus according to the present invention.

Of course, without prejudice to the principle of the invention, thedetails of implementation and the embodiments may vary widely withrespect to what is described and illustrated herein, without therebydeparting from the scope of the present invention, as defined by theannexed claims.

All of the above U.S. patents, U.S. patent application publications,U.S. patent applications, foreign patents, foreign patent applicationsand non-patent publications referred to in this specification and/orlisted in the Application Data Sheet, are incorporated herein byreference, in their entirety.

The above description of illustrated embodiments, including what isdescribed in the Abstract, is not intended to be exhaustive or to limitthe invention to the precise forms disclosed. While specific embodimentsand examples are described herein for illustrative purposes, variousequivalent modifications are possible within the scope of the inventionand can be made without deviating from the spirit and scope of theinvention.

These and other changes can be made in light of the above-detaileddescription. In general, in the following claims, the terms used shouldnot be construed to be limiting to the specific embodiments disclosed inthe specification and the claims, but should be construed to include allsystems, devices and/or methods that operate in accordance with theclaims. Accordingly, the invention is not limited by the disclosure, butinstead its scope is to be determined entirely by the following claims.

1. A method for executing, as a function of a received signal, aprocedure of channel estimation of a transmission channel with memory intelecommunications systems, the method comprising: estimating a delayspread associated to said channel, said estimating the delay spreadincluding calculating a root mean square value of delay spread byevaluating crossings with a threshold level of a characteristic curve ofa transfer function representing said channel, said evaluating ofcrossings including evaluating a first number of crossings,corresponding to a real part of said transfer function, and a secondnumber of crossings, corresponding to an imaginary part of said transferfunction, with the threshold level corresponding to a zero level; andapplying a mean operation to said first number of crossings and saidsecond number of crossings, to obtain a mean number of crossings.
 2. Themethod according to claim 1 wherein said root mean square value of delayspread is obtained, via a relation of direct proportionality, from saidmean number of crossings.
 3. The method according to claim 1 whereinsaid root mean square value of delay spread is obtained by calculating aroot mean square value of said mean number of crossings but for acorrective factor that takes into account a contribution of noise on thecalculation of the crossings with said zero level, said correctivefactor being proportional to an inverse of a signal-to-noise ratio. 4.The method according to claim 1, further comprising: obtaining a valueof rough estimation of the channel by demodulating the received signal;calculating said root mean square value of delay spread according tosaid value of rough estimation of the channel; and supplying said rootmean square value of delay spread to an operation involving fine channelestimation.
 5. The method according to claim 1 wherein saidtelecommunications system operates according to an OFDM modulation. 6.The method according to claim 1 wherein said telecommunications systemis a system of a wireless type, including an IEEE 802.11a WLAN standardor an Hyperlanll WLAN standard.
 7. An apparatus for performing, as afunction of a received signal, a channel estimation in a transmissionchannel with memory in a telecommunications system, the apparatuscomprising: a module configured to estimate a delay spread associated tosaid channel, by calculating a root mean square value of delay spread byevaluating crossings with a threshold level of a quantity associated toa transfer function representing said channel, said module is configuredto perform said evaluation of crossings by evaluating a first number ofcrossings, corresponding to a real part of said transfer function, and asecond number of crossings, corresponding to an imaginary part of saidtransfer function, with the threshold level corresponding to a zerolevel, and said module further being configured to apply a meanoperation on said first number of crossings and said second number ofcrossings to obtain a mean number of crossings.
 8. The apparatusaccording to claim 1 wherein said module configured to estimate thedelay spread associated to said channel is configured to calculate saidroot mean square value of delay spread via a relation of directproportionality from said mean number of crossings.
 9. The apparatusaccording to claim 7 wherein said module configured to estimate thedelay spread associated to said channel is configured to calculate saidroot mean square value of delay spread by calculating a root mean squarevalue of said mean number of crossings but for a corrective factor thattakes into account a contribution of noise on the calculation of thecrossings with said zero level, said corrective factor beingproportional to an inverse of a signal-to-noise ratio of the channel.10. The apparatus according to claim 7, further comprising: a firstmodule configured to calculate a value of rough estimation of thechannel by demodulating the received signal and to supply said value ofrough estimation to said module configured to estimate a delay spread asa function of said value of rough estimation; and a second module offine channel estimation that receives said value of RMS-DS.
 11. Theapparatus according to claim 7 wherein the module comprises part of areceiver for OFDM telecommunications systems.
 12. The apparatusaccording to claim 7 wherein said module comprises part of a receiver ofa wireless telecommunications system, including a receiver compatiblewith an IEEE 802.11a WLAN standard or a Hyperlanll WLAN standard.
 13. Anarticle of manufacture, comprising: a computer-program product that canbe loaded into a memory of a computer and having portions of softwarecode for implementing channel estimation of a communication channel whenthe product is run on the computer, by: estimating a delay spreadassociated to said channel according to a root mean square value ofdelay spread based on crossings of a characteristic curve of a transferfunction representing said channel, at least some of the crossings beingassociated with a threshold level; evaluating a first number ofcrossings, corresponding to a real part of the transfer function, and asecond number of crossings, corresponding to an imaginary part of saidtransfer function, with the associated threshold level of the crossingscorresponding to a zero level; and applying a mean operation, to thefirst number of crossings and to the second number of crossings, toobtain a mean number of crossings.
 14. The article of manufacture ofclaim 13 wherein the computer-program product further has portions ofsoftware code for determining the root mean square value of delay spreadfrom the mean number of crossings using a direct proportionalityrelation.
 15. The article of manufacture of claim 13 wherein thecomputer-program product further has portions of software code fordetermining the root mean square value of delay spread by calculating aroot mean square value of the mean number of crossings, along with acorrective factor to account for noise contribution.
 16. The article ofmanufacture of claim 13 wherein the computer-program product further hasportions of software code for: obtaining a value of rough estimation ofthe channel by demodulating a received signal; determining said rootmean square value of delay spread according to the value of roughestimation of the channel; and supplying the root mean square value ofdelay spread to an operation involving fine channel estimation.
 17. Asystem to perform channel estimation of a communication channel, thesystem comprising: a module adapted to estimate a delay spreadassociated with the channel according to a root mean square value ofdelay spread, the root mean square value of delay-spread being based oncrossings with a threshold level of a quantity associated with atransfer function representing the channel, wherein the module isadapted to evaluate the crossings by evaluating a first number ofcrossings, corresponding to a real part of the transfer function, and asecond number of crossings, corresponding to an imaginary part of thetransfer function, with the threshold level of the crossingscorresponding to a zero level, and wherein the module is further adaptedto apply a mean operation on the number of crossings and on the secondnumber of crossings to obtain a mean number of crossings that can beused to estimate the delay spread associated with the channel.
 18. Thesystem of claim 17 wherein the module is adapted to estimate the delayspread associated with the channel, using the mean number of crossings,based on a direct proportionality relation.
 19. The system of claim 17wherein the module is adapted to determine the root mean square value ofdelay spread by calculating a root mean square value of the mean numberof crossings, along with a corrective factor to account for noisecontribution.
 20. The system of claim 17, further comprising: a firstunit to obtain a value of rough estimation of the channel bydemodulating a received signal; a second unit communicatively coupled tothe first unit to determine the root mean square value of delay spreadaccording to the value of rough estimation of the channel obtained bythe first unit; and a third unit coupled to the second unit to performfine channel estimation based on the root mean square value of delayspread.